Probability Distributions and Bayesian Inference

Transcript

1. PROBABILITY DISTRIBUTIONS AND Bayesian Inference
2. “Humans are very bad at understanding probability. Everyone finds it difficult, even I do.”
3. Random Variables A THING THAT CAN TAKE ON A BUNCH OF DIFFERENT VALUES
4. PROBABILITY DISTRIBUTIONS A lookup for how likely each outcome is
5. Probability Density Functions A LOOKUP FOR CONTINUOUS-VALUED RANDOM VARIABLES
6. PROBABILITY MASS FUNCTIONS A lookup for discrete-valued random variables
7. INTO THE SUNSET WITH A PDF AT MY SIDE Of a PDF, we ask questions. All the questions. And get all the answers.
8. YOUR BROTHER BUILDS A PAINTBALL MACHINE
9. EMPIRICAL DISTRIBUTIONS WHAT'S HAPPENED SO FAR FROM THE OUTSIDE LOOKING IN
11. THEORETICAL DISTRIBUTIONS What's really going on from the inside looking out
14. STATISTICAL INFERENCE SMASHING THE WALL
15. BAYESIAN Inference
19. INFERENCE
20. MCMC Markov Chain Monte Carlo
21. 1. Start at current position 2. Propose moving to a new position (investigate a pebble near you) 3. Accept/reject new position if the new pebble "likely came from the mountain" 4. If you accept, move to the new position and return to Step 1. If you reject, stay at current position and return to Step 1 5. After many iterations, return all accepted pebbles
22. EXAMPLE: PAINTBALL INFERENCE
23. EXAMPLE: CUSTOMER CARE CALL VOLUME CHANGE-POINT DETECTION
24. SOURCES BAYESIAN METHODS FOR HACKERS MCMC SAMPLING FOR DUMMIES